Deformation and stability of a viscous electrolyte drop in a uniform electric field

Abstract

We study the deformation and breakup of an axisymmetric electrolyte drop which is freely suspended in an infinite dielectric medium and subjected to an imposed electric field. The electric potential in the drop phase is assumed small, so that its governing equation is approximated by a linearized Poisson-Boltzmann or modified Helmholtz equation (the Debye-Hückel regime). An accurate and efficient boundary integral method is developed to solve the low-Reynolds-number flow problem for the time-dependent drop deformation, in the case of arbitrary Debye layer thickness. Extensive numerical results are presented for the case when the viscosity of the drop and surrounding medium are comparable. Qualitative similarities are found between the evolution of a drop with a thick Debye layer (characterized by the parameter χ ≪ 1, which is an inverse dimensionless Debye layer thickness) and a perfect dielectric drop in an insulating medium. In this limit, a highly elongated steady state is obtained for sufficiently large imposed electric field, and the field inside the drop is found to be well approximated using slender body theory. In the opposite limit χ ≫ 1, when the Debye layer is thin, the drop behaves as a highly conducting drop, even for moderate permittivity ratio Q = ǫ 1 /ǫ 2 , where ǫ 1 , ǫ 2 is the dielectric permittivity of drop interior and exterior, respectively. For parameter values at which steady solutions no longer exist, we find three distinct types of unsteady solution or breakup modes. These are termed conical end formation, end splashing, and open end stretching. The second breakup mode, end splashing, resembles the breakup solution presented in a recent paper [R. B. Karyappa et al., J. Fluid Mech. 754, 550-589 (2014)]. We compute a phase diagram which illustrates the regions in parameter space in which the different breakup modes occur.

Numerical and asymptotic analysis of the three-dimensional electrohydrodynamic interactions of drop pairs

“…The complicated interplay between the electrostatic and viscous fluid stresses results in either oblate or prolate drop deformation in weak fields (Taylor 1966), and a complex dynamics in strong fields, such as break-up (Torza, Cox & Mason 1971; Sherwood 1988; Lac & Homsy 2007; Karyappa, Deshmukh & Thaokar 2014; Lanauze, Walker & Khair 2015; Pillai et al. 2016; Wang, Ma & Siegel 2019), streaming either from the drop poles (Taylor 1964; de la Mora 2007; Collins et al. 2008, 2013; Herrada et al.…”

“…The electric field acting on this induced surface charge creates tangential electric stress, which shears the fluids into motion. The complicated interplay between the electrostatic and viscous fluid stresses results in either oblate or prolate drop deformation in weak fields (Taylor 1966), and a complex dynamics in strong fields, such as break-up (Torza, Cox & Mason 1971;Sherwood 1988;Lac & Homsy 2007;Karyappa, Deshmukh & Thaokar 2014;Lanauze, Walker & Khair 2015;Pillai et al 2016;Wang, Ma & Siegel 2019), streaming either from the drop poles (Taylor 1964;de la Mora 2007;Collins et al 2008Collins et al , 2013Herrada et al 2012;Sengupta, Walker & Khair 2017) or equator (Brosseau & Vlahovska 2017;Wagoner et al 2020) and electrorotation (Ha & Yang 2000;Salipante & Vlahovska 2010Das & Saintillan 2017).…”

Ion emission from nanodroplets undergoing Coulomb explosions: a continuum numerical study

“…2006; Fontelos, Kindelán & Vantzos 2008; Gawande et al. 2017; Wang, Ma & Siegel 2019; Gawande et al. 2020) and values near observed in experiments (Duft et al.…”

Micromixing with In-Flight Charging of Polymer Solutions in a Single Step Enables High-Throughput Production of Micro- and Nanofibers

“…Indeed, some of the micrometer-sized globular structures show relics evidencing filament ejection from their surfaces, thus indicating that at some point the globular structures developed surface instabilities because of their charge. 49 , 50 Such instabilities led to the formation of so-called Taylor cones followed by expulsion of mass in the form of a thin jet which quickly dried. Figure 4 b shows an SEM image depicting typical fibrous structures produced with the MIC approach, where also randomly oriented straight microfibers and BOAS of varying sizes (red rectangle and blue oval) are observed.…”

“…In this case, the fibrous structure contained several globular structures (Figure a), implying that despite the charging and application of the electric field a fraction of the filaments not only did not elongate (because of high flow rate and short t R ) but also did not breakup and rather formed the irregular structures, most probably because of the viscoelasticity of the solution. Indeed, some of the micrometer-sized globular structures show relics evidencing filament ejection from their surfaces, thus indicating that at some point the globular structures developed surface instabilities because of their charge. , Such instabilities led to the formation of so-called Taylor cones followed by expulsion of mass in the form of a thin jet which quickly dried. Figure b shows an SEM image depicting typical fibrous structures produced with the MIC approach, where also randomly oriented straight microfibers and BOAS of varying sizes (red rectangle and blue oval) are observed.…”